Question

nasam of Length breadth and height of a cuboid is 19 cm and length of its diagonal is 11 cm find the surface area​

Answer 1

$\huge\sf\fbox\purple{ ♡ Solution ♡ }$

Length of diagonal of cuboid =l2+b2+c2

Surface area of cuboid =2(lb+bh+hl)

Assume -

⇒length=l

    Breadth=b

    Depth=h

Given eq (1) l+b+h=19

eq (2) length of diagonal =11

⇒l2+b2+h2=11

Simplifying eq (2)

⇒l2+b2+h2=121

Taking (l+b+h)2=l2+b2+h2+2lb+2bh+2lh

substituting values

⇒(19)2=121+2(lb+bh+lh)

⇒361−121=2(lb+bh+lh)

⇒240=2(lb+bh+lh)

∴ Surface area of cuboid =240.

Answer 2

❤️Anu❤️

ʟᴇɴɢᴛʜ ᴏғ ᴅɪᴀɢᴏɴᴀʟ ᴏғ ᴄᴜʙᴏɪᴅ =ʟ2+ʙ2+ᴄ2

sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ ᴏғ ᴄᴜʙᴏɪᴅ =2(ʟʙ+ʙʜ+ʜʟ)

ᴀssᴜᴍᴇ -

⇒ʟᴇɴɢᴛʜ=ʟ

    ʙʀᴇᴀᴅᴛʜ=ʙ

    ᴅᴇᴘᴛʜ=ʜ

ɢɪᴠᴇɴ ᴇǫ (1) ʟ+ʙ+ʜ=19

ᴇǫ (2) ʟᴇɴɢᴛʜ ᴏғ ᴅɪᴀɢᴏɴᴀʟ =11

⇒ʟ2+ʙ2+ʜ2=11

sɪᴍᴘʟɪғʏɪɴɢ ᴇǫ (2)

⇒ʟ2+ʙ2+ʜ2=121

ᴛᴀᴋɪɴɢ (ʟ+ʙ+ʜ)2=ʟ2+ʙ2+ʜ2+2ʟʙ+2ʙʜ+2ʟʜ

sᴜʙsᴛɪᴛᴜᴛɪɴɢ ᴠᴀʟᴜᴇs

⇒(19)2=121+2(ʟʙ+ʙʜ+ʟʜ)

⇒361−121=2(ʟʙ+ʙʜ+ʟʜ)

⇒240=2(ʟʙ+ʙʜ+ʟʜ)

∴ sᴜʀғᴀᴄᴇ ᴀʀᴇᴀ ᴏғ ᴄᴜʙᴏɪᴅ =240.

Step-by-step explanation:

l hope it will help u ☺️✌️☺️